I did a lesson on lateral thinking earlier this spring.
First, I gave a quick little Wikified definition of lateral thinking. I then gave them this problem to solve: A man lives on the 18th floor. Every day, he goes out for a walk. When he comes home, he takes the elevator up to the 13th floor, then walks up to the 18th... unless it's raining or there's another person with him, then he rides the elevator to the 18th. Why?
I also had them try to figure out how to make a car work with square wheels and then try to apply the square wheels car solutions to a real car.
For the Last 10 People equivalent, I tell them that they're going to be stranded on a desert island for an unknown period of time (anywhere from one day to a lifetime) and they can take 5 items each (but place limits, they must specify the amount of food if they're going to take food... ridiculous amounts count as multiple items). They must debate over which items are most needed for the group to survive. Oddly, one group decided to take a rice cooker.
Hope that helps... I'll share more details if you want once I get my former coworker to email me all of my old lesson plans.